There are several answers to this question as the term 'analog' (or 'analogue') has different meanings in different contexts.

In less formal contexts, the term 'analog' is often used to describe a substance which has major chemical structures in common with another chemical. One might say, imprecisely, that Mescaline is an analog of MDMA or that L-Tryptophan is an analog of Psilocybin, because at first glance, these pairs seem to have many similarities in chemical structure.

But to people familiar with organic chemistry, the term 'analog' has a more precise meaning. Many chemicals that look alike and have similar chemical structures react very differently both in and out of the body. L-Tryptophan, an essential dietary amino acid (without which humans would die), is superficially very similar to psilocybin. However, in the field of chemistry, these two chemicals do not qualify as analogs. Here, 'analog' is used to describe two chemical molecules which differ only by the transposition of one atom or simple functional group for another (ie replacing a bromine with iodine, or a hydrogen with a methyl group). In the chemistry definition, Psilocybin and Tryptophan are definitely not analogs, despite their many similarities.

The reason the issue of chemical analogs is important to most people, however, is because the U.S. Federal Government (among many others) chose to create yet another formal meaning by encoding a definition into federal law. This was done to try to make it easier to prosecute producers and retailers of recreational psychoactive drugs. The Federal Analogue Act of 1986 created disasterous confusion by re-defining the word 'analog' in a very imprecise manner for the purposes of the Act. The complicated history of the bill can be found elsewhere, but the final version of the law was written confusingly and overly broadly.

The Federal Analogue Act defines an analog as a substance which is 'substantially similar' to a scheduled substance and has either an effect 'similar to or greater than' a controlled substance or is thought to have such an effect. The law fails to define what 'substantially similar' means, nor does it try to clarify what would constitute a 'similar or greater' effect.

The explicit intention of Congress when they created the law was to be able to allow the DEA to arrest and prosecute underground chemists who make minor changes to an existing illegal chemical, resulting in a new chemical which can be sold as a recreational drug but which is not specifically listed as illegal. Because the law is written so broadly and vaguely, however, it is considered by experts in the field of psychoactive chemistry to be one of the most oppressive laws ever written, making the very creation of a new, unknown and untested chemical, illegal.

The Analogue Act is also sometimes referred to as the 'Designer Drug Law'. The term "Design Drug" was popularized in the 1980's by the media and used by law makers to stir up excitement about the perceived threat of these new chemicals. Part of the reason that "Designer Drugs" were so frightening is that in the early 1980's, there were a number of very serious injuries and deaths associated with a contaminant (MPTP) in a new underground chemical called MPPP. The renewed energy which the Reagan administration brought to the War on Drugs brought out renewed vigor in the underground markets and there was a fear that traditional regulatory schemes were not able to keep up with the widening array of psychoactives.

Other countries and most U.S. states have their own definition of what an analog means, as many have created their own versions of the Analogue Act.

So, to answer your question directly, if a chemical is an analog of another, it can mean different things depending on the context in which it is said. If it said by a lay person in casual conversation, it could mean that they are saying the chemicals share large common features or if the term is being used precisely it could mean that the chemicals vary by a single atom or small structure, or it could mean that the chemical might meet some legislated definition of being 'substantially similar' to a controlled substance and thus itself be illegal to possess without a prescription or license.

The US Federal Analogue Act has 3 parts:

'chemical substantially similar'

AND EITHER

effects similar to substance in Schedule I or II

OR

someone represents it as having the effect of a controlled substance

In the law that was put on the books federally, there were no connectives between these, but the only published case law on this topic courts have ruled that what Congress -meant- was : 1 AND either 2 or 3. So the substance must have an 'analog' structure to count. Unfortunately, to repeat, the law does not define what they mean by 'substantially similar'.

Another strange twist in the story of the Federal CSA is that when the law was first approved, the printed version included the "AND" conjunction after the first clause and this word mysteriously disappeared between its preliminary approval and final printing in the Federal Register.

The DEA defines it this way:

A controlled substance analogue is a substance which is intended for human consumption and is structurally or pharmacologically substantially similar to or is represented as being similar to a Schedule I or Schedule II substance and is not an approved medication in the United States. from deadiversion.usdoj.gov, Nov 2001

Here is an excerpt from the Shulgins' excellent TIHKAL on the subject:

This legislation is called 'the Controlled Substance Analogue Enforcement Act of 1986' and is part of Public Law 99-570. It was signed into law on October 27, 1986, just days before the national elections, and the news and ramifications of it have been largely lost in the noise and drama of the political events of the time. I personally believe that this law presents a shameful barrier to a very important segment of scientific research.

Let me dissect this law into its two major parts. What is an analogue? And what is the behaviour, involving an analogue, that is criminal?

According to this law, a drug is an analogue if it meets any one of the following criteria:

First, the chemical structure of the drug is considered. The compound is an analogue if its structure is substantially similar to the structure of any listed Schedule I or II drug. Just what are the structures of the drugs that are contained in these two schedules? You can find a complete spectrum of functional groups. All four types of amines are present; primary amines, secondary amines, tertiary amines, and quarternary ammonum salts. All three types of alcohols are present; primary alcohols, secondary alcohols, and tertiary alcohols. There are acids, esters, ethers, amids, ketones, and nitriles.

There are examples of all the most common heterocyclic ring systems, such as pyridines, piperidines, pyrrolidines, indoles, imidazoles, morpholines, thiophenes, furans, pyrans, quinazolines, dioxoles, oxazolines, pyrimidines, and purines. And of course, there are simple benzene-ring aromatic compounds and there are simple non-benzene-ring aliphatic compounds including cyclopropyl rings, cyclobutyl rings, cyclopentyl rings, and cyclohexyl rings. One would be hard put to find a structure of any drug, anywhere, which could not be argued by some person, somewhere, as being in some way structurally related to a Schedule I or a Schedule II drug.

And what was the reason for the use of the intentionally vague phrase "substantially similar"? There is a term in rhetoric knows as a disclaimer, a word introduced as a hedge or a qualification, a word chosen to allow a certain freedom of interpretation. Words or phrases such as almost, probably, approximately, in a few days, in two weeks at the latest, are disclaimers. There is a measured ambiguity in the phrase "similar to" and there is a measured ambiguity in the phrase "substantially the same as." But what is to be inferred from "substantially similar"? Suddenly, the exactness, the precision of the original Controlled Substances Act, with its explicitly named drug targets, had been totally compromised.

A second, independent definition of an analogue deals with its pharmacological action. A drug is to legally considered as an analogue if it has a stimulant, depressant, or hallucinogenic action that is substantially similar to that of a Schedule I or Schedule II drug. In short, any drug which affects the CNS (central nervous system) in any of these ways, or in ways that could be construed as being "substantially similar" to those evoked by a scheduled drug, becomes an analogue within this legal definition. Again, the vague double disclaimer "substantially similar" must be reckoned with as part of the description.

A third definition is an extension of this, and involves the way a drug is represented. If a material is intentionally represented as having a stimulant, depressant, or hallucinogenic action that is substantially similar to that of a Schedule I or Schedule II drug, it becomes an analogue.

It is generally accepted that if two of these three definitions are met then the chemical or drug in question becomes a controlled substance analogue. The law explicitly states that there are four criteria, any of which will exclude it from becoming an analogue; if it is already a controlled substance, if it has an approved drug application, if a particular person has an exemption allowing him investigational use of that drug in question, or it is not intended for human consumption.

And what is the nature of one's behaviour with an analogue that shall constitute a criminal act? It is the intent to make it available for human consumption. And if such were to occur, the analogue would be treated as if it were a Schedule I drug.